Now, on to trouble shooting. You have to turn the volume up nearly all the way to get a tiny amount of sound. And the sound you get sounds muffled and distorted. What might be giving me trouble, or what tests can I run to narrow down the problem? It could be my poor soldering skills, diaphragm not tensioned enough, or something else completely.

Note: I read that ESL's can be dangerous, and they give you quite a shock if you touch them. Right after I hooked up the speaker, while my back was turned, my Dad walks up and starts touching the speaker. No shock. Perhaps that is my problem.

I would first trace all of the connections and verify them to the schematic. It could be something as simple as as reversed connection to one of the step up transformers or the little transformer in the power supply, or a reversed diode in the power supply. I was helping a buddy of mine build some speakers once and he had reversed a connection to the power supply transformer; which immediately shorted out the affected winding as soon as we powered up the circuit -- had to replace that transformer).

If the wiring looks OK, I would then check to verify that the power supply is putting out. You can't check the power supply output voltage with a standard DVM unless you have an HV probe with it (that much voltage would burn out most DVM's). What you can do--- and please be DAMN CAREFUL not to electrocute yourself-- is, with power off, tap into or disconnect the lead from the power supply to the center-tap of the step-up transformers, and also tap into or disconnect the lead from the power supply to the diaphragm. Then, power up the power supply, and just brush those two lead ends together-- you should get a nice spark if the power supply is working. The output resistor may not pass enough current to give a visible spark so you may need to bypass it with a jumper to do this test. Again--- be very careful not to touch any uninsulated portion of the wires--especially if you bypass the output resistor, as you could then get potentially lethal current out.

BTW, you can safely touch one stator while the panel is playing but it's very risky to touch both stators while the panel is playing!

Can you post a close up of your transformer interface block it would be easier to see if they are wired correctly.
From the sound of the video it seems as one of them is out of phaze with the other.
the distortions that you are hearing is what is left over frome the transformers saturating and/or the amplifier clipping from it being so high.

I get absolutely nothing when I hook mine out of phaze.

Do make sure that your bias supply is working as Charlie Mentioned if it is not working than you will get little sound out of the panel as well just like the video.

Make sure that all of the diodes are going in the proper sequence of direction as this can get confusing at times I have done this myself a few times.

You can check the supply with an arc test,Just make sure that you are insulated from any of the feed wires and that you are using the ground wire to probe with.
I usually use a screwdriver connected to the ground to do this.
always use a series current limiting resistor of at least 1 megohm as well from the output of the voltage divider.
If you don't then pulling an arc could cause an an over current draw causing a diode or few to short if they are of the low amperage types and they would have to be replaced.
This I have done as well.

You can also make your own voltage divider to measure the voltage out of your supply as well by using a bunch of 10megohm resistors in series.

Thank you very much for the input. I basically threw them together because I was under a time constraint, so I am sure if I spend some time I can find and correct the problem. It will be some time before I have a chance to work on the speaker, but I will surely update this thread when I get to them.

if the polarization doesn´t charge the membrane You may be tempted to push up the volume, thereby creating distortions, because even a non-polarized membrane will give a tiny bit of output. Check the membrane when switching on the polarizing supply. It should be pulled towards one of the stators. The deflection may be easily viewed as a reflection of a light torch.
Also, at the first couple of switch-ons most panels will release some low level tickling noises, the so called ´birth-cry´. If the membrane doesn´t deflect or the panel keeps totally quiet, the chance is high that the membrane isn´t charged up at all.
I always test the charge-up without the second stator, ie. the open panel to be able to recoat the diaphragm or the contact point if necessary.

I have never tried dish soap I know other have used it with limited success.
You would be better off using a staticide type product like Licron and Licron Crystal or some prefer staticide 6300.
Shelf life seems to be an issue with the latter.

If you want to try a DYI type of coating, many report good results using a coating made from PVA (white) glue.
I have experimented with mixtures using this method and found that I needed to use a little (a few drops, 3 or4 or so per 2 onces) dish soap (Dawn) to cause the mixture (1:5 to 1:10 ,glue/water) to wet the mylar properly with out beading up.
Once it is dried it leaves a very very thin and almost transparent coating on the diagphram.
Although I personally have not used this method yet but others have and report that it works well.
I have messed with it though and have documented my experiments in one of these threads with many closeup photos of the coating results .
I still have two nearly full cans of both of the techspray products and is why I haven't tried it yet.
I rarely have to replace any diagphrams (only due to burn holes in them).
The last one I had just burned up was one of the original diagphrams that I had made in 2003 with the orginal formula licron spary and it had worked flawlessly every time I powered up the panel.